There's an old debate going on in the guitar community about how much does wood choice and body shape affect the sound of an electric guitar. No one denies that there's a difference acoustically (how the guitar sounds unplugged) because in this situation it's the wood and body shape that amplify the sound made by string vibrations, but when we're talking about the sound as it comes from the pickups, things get much more uncertain because there are a lot of variations even in supposedly identical guitar parts, and accounting for all of them for the purpose of doing an experiment where the only difference between two guitars is the wood is difficult (I certainly haven't heard of an experiment that was satisfying enough, but feel free to prove me wrong). I'm interested in a way to circumvent these practical difficulties using a theoretical explanation:
Since the pickup only sees the string's vibrations, the question basically becomes "does body shape and wood make enough difference in the way a string vibrates that it changes the sound in a noticeable way", and this sounds like something that may be possible to figure out mathematically, or at the very least should be much easier to test because there are less variables involved. My question is:
Is what I'm describing possible to calculate/test, and has this been done before?